Controlling subdivision surfaces quality
There are some methods to do so:


Using edge crease (ShiftE);
Adding suppport edge loops (CtrlR);
Marking sharp edges (CtrlE > Mark Sharp), then add a Solidify modifier BEFORE Subsurf modifier.




Each way has pros and cons, choose one or more to meet the needs.

The above is for shaping in modifier level. However, the resolution cannot be controlled in this level. You may consider to apply modifier first, then select all elements (or particular area) in Edit Mode, X > Limited Dissolve, set the dissolve angle in F6 panel.

Tip: To select faces that are co-planar or nearly co-planar, you can select one or more faces, ShiftG > Co-planar, tweak Threshold in kbd>F6 panel.